Question

  ​(Bond valuation) A bond that matures in 8 years has a ​$1,000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 18 percent.

What would be the value of this bond if it paid interest​ annually?

What would be the value of this bond if it paid interest​ semiannually?

*Someone previously answered this with annually = $604.56 and semiannually = $596.89 and the annual number is incorrect*

Answer 1

Annual compounding

Information provided:

Par value= future value= $1,000

Time= 8 years

Coupon rate= 9%

Coupon payment= 0.09*1,000= $90

Yield to maturity= 18%

The value of the bond is calculated by computing the present value of the bond.

Enter the below in the financial calculator:

FV= 1,000

N= 8

PMT= 90

I/Y= 18

The value obtained is 633.02.

Therefore, the value of the bond is $633.02 if interest is annually compounded.

Semi-annual compounding

Information provided:

Par value= future value= $1,000

Time= 8 years*2= 16 semi-annual periods

Coupon rate= 9%/2= 4.5%

Coupon payment= 0.045*1,000= $45

Yield to maturity= 18%/2= 9%

The value of the bond is calculated by computing the present value of the bond.

Enter the below in the financial calculator:

FV= 1,000

N= 16

PMT= 45

I/Y= 9

The value obtained is 122.20.

Therefore, the value of the bond is $122.20 if interest is semi-annually compounded.

In case of any query, kindly comment on the solution.